Using the EVE Forums to officially (aka legally) buy a character is always the cheapest, as long as you are patient. People whom are leaving the game and can not stomach all of the years of hard work (well… PLAY - Hahah) going to waste, will sell their awesome toons for less than what you can train one for. Every now and then you can find a 2003 original years toon. Those have a base value of 50b with no skills. But yeah, you said cheapest way… It’s the buy and sell forums for sure.
Additionally, injectors provide a poor return as your skill points increase. By the time you get all racial ship skills up to cruiser to 5, plus all support skills, drone, weapon, etc, each injector only gives 150k skill points greatly hindering growth through injectors.
I would recommend buying a toon and only using injectors to finish off skills the toon does not have but you think are key.